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My theory is that odd numbers (except 1) will never reach 1, and only powers of 2 will reach 1. Why? First of all after some trial and error, I realized that many of the odd numbers squared + 1 are not powers of 2. If the odd number squared + 1 is not a power of 2, it will redo the process of n^2 + 1. However, if it is a power of 2, then it will reach 1. But trial and error says elsewise and n^2 + 1 won't be a power of 2 (idk if that's a theorem). Thus the only integers from 1 - 100 will be 1, 2, 4, 8, 16, 32, and 64. So 7 of them...

Please repost the question but this time take away the dollar signs and use the latex function in the website.. it is a bit illegible rn.. thx

The answer is approximately 114.357 (read the 9/26 post)

Time to tackle this tough reposted question! 

By pythagorean theorem, CE = sqrt(30^2 - 22^2) - 10. CE = 4sqrt(26) - 10. Then by pythagorean theorem, AE = sqrt(22^2 + 10^2) = 2sqrt(146). Now we know the side lengths of triangle ACE are 30, 4sqrt(26) - 10, and 2sqrt(146) respectively. Using heron's formula, the area of triangle ACE would approximately be 114.357.

f(-x)/2 compared to f(x) is compacting f(x) by a factor of 2, and the f(-x) is flipping it across the y axis. However if we are trying to find the area between the figure to the x axis, flipping across the y axis is irrelevant, thus all we care about is how it got compacted. If the original area was 10 units, and we smushed it by a factor of 2, then the base would remain constant but the height would be half of it. Idk what the figure looks like, but the answer is probably 10/2 = 5.

If makayla has 8$ to buy tickets at the school fair (I think you accidentally clicked enter), and each ticket costs 1.5$, then floor of 8/1.5 would be the MAX amount of tickets she could buy (5 physical tickets). The inequality with variable t (amount of tickets) would be:

1.5t <= 8, where t is a nonnegative integer.

There are 4 suites, and 13 cards of each kind. That means there are 4 9s and 13 Spades. Of those 13 Spades, 12 are not 9s and 1 is a 9, thus we are overcounting, so there are 4 + 13 - 1 Spades or 9s in the deck. 16

Use the angle bisector theorem! Set AZ = x and BZ = 8 - x. Can you use this theorem from here?

Hi Proyaop

Why do you think that this function is even. It does not say so in the question.

How can you know what   f(-x) looks like at all?

Firstly, it would be polite to respond after each time someone answers a question. Especially when it is a 'real' answer.

** You already asked this question in its non-proofed form and I answered.

Secondly, if you copy the whole question into google you will get several readily available answers.

Hello Guest!

\(\dfrac{ab}{c}=\dfrac{\dfrac{7}{4}\cdot \dfrac{11}{5}}{\dfrac{7}{2}}=\dfrac{\dfrac{77}{20}}{\dfrac{7}{2}} =\dfrac{77\cdot 2}{20\cdot 7}=\color{blue}\dfrac{11}{10}\)

  !

You qare coprreect thank you!

Lol this is AoPS algebra 2 math homework... I will not say the answer, but I will be saying a hint. 1/2 is halving the height of the object, and reflecting across the y axis won't do anything... Thus use geometry. 

Hi JoelKananelo!

Remember Pascal's triangle  (These numbers are the coefficients!)

                                                              1                      (a+b)^0

                                                            1   1                  (a+b)^1

                                                         1    2     1              (a+b)^2

                                                      1    3     3      1            (a+b)^3

                                                    1    4     6      4   1            (a+b)^4

                                                  1   5  10   10    5   1            (a+b)^5

                                                 1  6   15  20  15   6   1              (a+b)^6

We are interested in the last row:

Let \(a=3x \\ b=-4y\)

Hence,

\((a+b)^6=a^6+6a^5b+15a^4b^2+20a^3b^3+15a^2b^4+6ab^5+b^6\)

So,

\((3x-4y)^6=(3x)^6+6(3x)^5(-4y)+15(3x)^4(-4y)^2+20(3x)^3(-4y)^3+15(3x)^2(-4y)^4+6(3x)(-4y)^5+(-4y)^6\)

Simplify this and you should get your answer!
I hope this helps :)

Thank you so much!  I think I understand this problem now!

If I've interpreted your question correctly, then , assuming that it's row1 replaced by row1 - 12*row2, we have
 

A → [4 - 12*(-6),   3 - 12*(-3),   0 - 12*12]

        [       -6,              -3,                 12    ]

I'll leave you to do the number crunching!

I do not think that you have proof read this.

I looked at scenarios.

If both red are on the outside triangle there are   3 ways to choose which

For each of those ere are  2 ways to place the other colours.  Equalling 2*3 = 6 ways

--------

If both reds are on the inside triangle there a 3 ways to chose the dots then 2 ways to place the other colours so that is another 6

----------

If one red is inside and the other outside then there are 3 ways to choose where then there are 4 ways to place the other colours = 3*4=12

----------

So I think that there are   6+6+12 = 24 ways.

I think the third and fourth ones are both right assuming order counts.

k

1)  Give k lolipops of different flavours to n kids, if each kid gets at most one lolipop.     

   Chose which k kids get a lolipop   that would be nCk  then decide who gets which lollipop that would be  k!

     so I think it is   nCk  *  k!

2) give k loliopops to n kids if kids can get any number of lolipops.    This is complicated and none of the above.

Hi Guest,

I'm not sure I understand your question. In case you're still around, could you try rephrasing your question?

Thank you!

Hi Guest,

Since a dictionary costs $12 before the discount, and we're trying to calculate the discount in dollar amounts...

We multiply the original price of the dictionary to the thirty percent that we're getting off.

Therefore,  \($12 \cdot \frac{30}{100}\)  will result in our answer.

Simplifying, our result is 

= \(\frac{$12*30}{100}\)

= \(\frac{$360}{100}\)

= \($3.6\)

\(\therefore\) The dollar amount of the discount we recieve is $3.6.

I hope this helped! Let me know if you have any questions :)

Week | Wins | Losses   

1                   3 

2                   6               

3                   9

4                   12

5            2      13

6            4       14

7            6        15

8            8         16

9            10        17

10           12       18

11          14         19

12          16         20

13           18        21

14           20       22

15           22       23

16           24       24

after 16 weeks, the team exactly won 24/48 (50%) of the total games, so n=16.